Self-similar solutions for the interaction of relativistic ejecta with an ambient medium

We find self-similar solutions to describe the interaction of spherically symmetric ejecta expanding at relativistic speeds with an ambient medium having a power law density distribution. Using this solution, the time evolution of the Lorentz factor of the outer shock is derived as a function of the explosion energy, the mass of the ejecta, and parameters for the ambient medium. These solutions are an ultra-relativistic version of the solutions for the circumstellar interaction of supernova ejecta obtained by Chevalier and extensions of the relativistic blast wave solutions of Blandford & Mckee.Comment: 12 pages, 1 figure, accepted for publication in Ap

Massive Black Holes in Star Clusters. I. Equal-mass clusters

In this paper we report results of collisional N-body simulations of the dynamical evolution of equal-mass star clusters containing a massive central black hole. Each cluster is composed of between 5,000 to 180,000 stars together with a central black hole which contains between 0.2% to 10% of the total cluster mass. We find that for large enough black hole masses, the central density follows a power-law distribution with slope \rho \sim r^{-1.75} inside the radius of influence of the black hole, in agreement with predictions from earlier Fokker Planck and Monte Carlo models. The tidal disruption rate of stars is within a factor of two of that derived in previous studies. It seems impossible to grow an intermediate-mass black hole (IMBH) from a M \le 100 Msun progenitor in a globular cluster by the tidal disruption of stars, although M = 10^3 Msun IMBHs can double their mass within a Hubble time in dense globular clusters. The same is true for the supermassive black hole at the centre of the Milky Way. Black holes in star clusters will feed mainly on stars tightly bound to them and the re-population of these stars causes the clusters to expand, reversing core-collapse without the need for dynamically active binaries. Close encounters of stars in the central cusp also lead to an increased mass loss rate in the form of high-velocity stars escaping from the cluster. A companion paper will extend these results to the multi-mass case.Comment: 15 pages, 8 figures, ApJ in pres

Simulation of Transitions between "Pasta" Phases in Dense Matter

Calculations of equilibrium properties of dense matter predict that at subnuclear densities nuclei can be rodlike or slablike. To investigate whether transitions between phases with non-spherical nuclei can occur during the collapse of a star, we perform quantum molecular dynamic simulations of the compression of dense matter. We have succeeded in simulating the transitions between rodlike and slablike nuclei and between slablike nuclei and cylindrical bubbles. Our results strongly suggest that non-spherical nuclei can be formed in the inner cores of collapsing stars.Comment: 4 pages, 4 figures, final version published in Phys. Rev. Lett., high-res figures can be seen at http://www.nordita.dk/~gentaro/research/fig

Self-Similar Evolution of Relativistic Shock Waves Emerging from Plane-Parallel Atmospheres

We study the evolution of the ultra-relativistic shock wave in a plane-parallel atmosphere adjacent to a vacuum and the subsequent breakout phenomenon. When the density distribution has a power law with the distance from the surface, there is a self-similar motion of the fluid before and after the shock emergence. The time evolution of the Lorentz factor of the shock front is assumed to follow a power law when the time is measured from the moment at which the shock front reaches the surface. The power index is found to be determined by the condition for the flow to extend through a critical point. The energy spectrum of the ejected matter as a result of the shock breakout is derived and its dependence on the strength of the explosion is also deduced. The results are compared with the self-similar solution for the same problem with non-relativistic treatment.Comment: 9 pages, 4 figures, To appear in The Astrophysical Journal Corrected typo

Roles of Supernova Ejecta in Nucleosynthesis of Light Elements, Li, Be, and B

Explosions of type Ic supernovae (SNe Ic) are investigated using a relativistic hydrodynamic code to study roles of their outermost layers of the ejecta in light element nucleosynthesis through spallation reactions as a possible mechanism of the "primary" process. We have confirmed that the energy distribution of the outermost layers with a mass fraction of only 0.001 % follows the empirical formula proposed by previous work when the explosion is furious. In such explosions, a significant fraction of the ejecta ($>$0.1 % in mass) have the energy greater than the threshold energy for spallation reactions. On the other hand, it is found that the outermost layers of ejecta become more energetic than the empirical formula would predict when the explosion energy per unit ejecta mass is smaller than \sim 1.3\times 10^{51}{ergs/}\Msun. As a consequence, it is necessary to numerically calculate explosions to estimate light element yields from SNe Ic. The usage of the empirical formula would overestimate the yields by a factor of \gtsim 3 for energetic explosions such as SN 1998bw and underestimate the yields by a similar factor for less energetic explosions like SN 1994I. The yields of light elements Li, Be, and B (LiBeB) from SNe Ic are estimated by solving the transfer equation of cosmic rays originated from ejecta of SNe Ic and compared with observations.Comment: 10 pages, 6 figures, 2 tables, to appear in The Astrophysical Journa

Light Element Production in the Circumstellar Matter of Energetic Type Ic Supernovae

We investigate energetic type Ic supernovae as production sites for Li6 and Be in the early stages of the Milky Way. Recent observations have revealed that some very metal-poor stars with [Fe/H]<-2.5 possess unexpectedly high abundances of Li6. Some also exbihit enhanced abundances of Be as well as N. From a theoretical point of view, recent studies of the evolution of metal-poor massive stars show that rotation-induced mixing can enrich the outer H and He layers with C, N, and O (CNO) elements, particularly N, and at the same time cause intense mass loss of these layers. Here we consider energetic supernova explosions occurring after the progeniter star has lost all but a small fraction of the He layer. The fastest portion of the supernova ejecta can interact directly with the circumstellar matter (CSM), both composed of He and CNO, and induce light element production through spallation and He-He fusion reactions. The CSM should be sufficiently thick to energetic particles so that the interactions terminate within its innermost regions. We calculate the resulting Li6/O and Be9/O ratios in the ejecta+CSM material out of which the very metal-poor stars may form. We find that they are consistent with the observed values if the mass of the He layer remaining on the pre-explosion core is 0.01-0.1 solar mass, and the mass fraction of N mixed in the He layer is about 0.01. Further observations of Li6, Be and N at low metallicity should provide critical tests of this production scenario.Comment: 12 pages, 2 figures, revised with referee suggestions, final version accepted in ApJ Letter

Self-similar solutions for the emergence of energy varying shock waves from plane-parallel atmospheres

We present a self-similar solution to describe the propagation of a shock wave whose energy is deposited or lost at the front. Both of the propagation of the shock wave in a medium having a power-law density profile and the expansion of the medium to a vacuum after the shock breakout are described with a Lagrangian coordinate. The Chapman-Jouguet detonation is found to accelerate the medium most effectively. The results are compared with some numerical simulations in the literature. We derive the fractions of the deposited/lost energy at the shock front in some specific cases, which will be useful when applying this solution to actual phenomena.Comment: 8 pages, 7 figures, to appear in Ap

Algorithm for Linear Response Functions at Finite Temperatures: Application to ESR spectrum of s=1/2 Antiferromagnet Cu benzoate

We introduce an efficient and numerically stable method for calculating linear response functions $\chi(\vec{q},\omega)$ of quantum systems at finite temperatures. The method is a combination of numerical solution of the time-dependent Schroedinger equation, random vector representation of trace, and Chebyshev polynomial expansion of Boltzmann operator. This method should be very useful for a wide range of strongly correlated quantum systems at finite temperatures. We present an application to the ESR spectrum of s=1/2 antiferromagnet Cu benzoate.Comment: 4 pages, 4 figure